共查询到20条相似文献,搜索用时 15 毫秒
1.
J. Hu 《Mathematische Zeitschrift》2000,233(4):709-739
Abstract. In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied
the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between
Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.
Received February 4, 1999 相似文献
2.
In this paper, one considers the change of orbifold Gromov–Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov–Witten invariants of symplectic orbifolds is proved. These results extend the results of manifolds case to orbifold case. 相似文献
3.
《中国科学 数学(英文版)》2015,(9)
We give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying relations in the tautological ring of the moduli space of2-pointed genus-3 stable curves. A byproduct of our search for genus-3 equations is a new genus-2 universal equation for Gromov-Witten invariants. 相似文献
4.
Brett Parker 《Advances in Mathematics》2012,229(6):3256-3319
This paper provides an introduction to exploded manifolds. The category of exploded manifolds is an extension of the category of smooth manifolds with an excellent holomorphic curve theory. Each exploded manifold has a tropical part which is a union of convex polytopes glued along faces. Exploded manifolds are useful for defining and computing Gromov–Witten invariants relative to normal crossing divisors, and using tropical curve counts to compute Gromov–Witten invariants. 相似文献
5.
Ignasi Mundet i Riera 《Topology》2003,42(3):525-553
In this paper we introduce invariants of semi-free Hamiltonian actions of S1 on compact symplectic manifolds using the space of solutions to certain gauge theoretical equations. These equations generalise both the vortex equations and the holomorphicity equation used in Gromov-Witten theory. In the definition of the invariants we combine ideas coming from gauge theory and the ideas underlying the construction of Gromov-Witten invariants. 相似文献
6.
XiaoWen Hu 《中国科学 数学(英文版)》2017,60(4):613-636
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol’nyi-Prasad-Sommerfield (BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande. 相似文献
7.
《中国科学 数学(英文版)》2017,(4)
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol'nyi-Prasad-Sommerfield(BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande. 相似文献
8.
We use the technique of Ruan (1999) and Li and Ruan (2001) to construct the virtual neighborhoods and show that the Gromov-Witten invariants can be defined as integrals over the top strata of the virtual neighborhoods. We prove that the invariants defined in this way satisfy all the axioms of Gromov-Witten invariants summarized by Kontsevich and Manin (1994).
相似文献9.
Combining elements of the b-calculus and the theory of elliptic boundary value problems, we solve the gluing problem for b-determinants
of Dirac type operators on manifolds with cylindrical ends. As a corollary of our proof, we derive a gluing formula for the
b-eta invariant and also a relative invariant formula relating the b-spectral invariants on a manifold with cylindrical end
to the spectral invariants with the augmented APS boundary condition on the corresponding compact manifold with boundary. 相似文献
10.
In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton’s relations on the moduli space of curves.As an application,we prove that Pixton’s relations imply a known topological recursion relation on Mg,1 for genus g≤4. 相似文献
11.
12.
Holger Spielberg 《Proceedings of the American Mathematical Society》2002,130(5):1257-1264
Hirzebruch surfaces provide an excellent example to underline the fact that in general symplectic manifolds, Gromov-Witten invariants might well count curves in the boundary components of the moduli spaces. We use this example to explain in detail that the counting argument given by Batyrev for toric manifolds does not work.
13.
I. G. Korepanov 《Theoretical and Mathematical Physics》2009,158(3):344-354
We generalize the construction of invariants of three-dimensional manifolds with a triangulated boundary that we previously
proposed for the case where the boundary consists of not more than one connected component to any number of components. These
invariants are based on the torsion of acyclic complexes of geometric origin. An adequate tool for studying such invariants
turns out to be Berezin’s calculus of anticommuting variables; in particular, they are used to formulate our main theorem,
concerning the composition of invariants under a gluing of manifolds. We show that the theory satisfies a natural modification
of Atiyah’s axioms for anticommuting variables.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 405–418, March, 2009. 相似文献
14.
Amitai Zernik 《Israel Journal of Mathematics》2014,200(1):297-325
Conformal field theories were first axiomatized by Segal (2004) as symmetric monoidal functors from a topological category of conformal cobordisms between compact oriented 1-dimensional manifolds to vector spaces. Costello (2007) later expanded the definition of the category to allow for cobordisms between manifolds with boundaries, and was able to use representations of this category to give a mirror partner for Gromov-Witten invariants. The main goal of this paper is to provide a rigorous definition of the category of open conformal cobordisms. To the best of our knowledge, such a definition does not appear in the literature. Although most results here are probably known to the experts, the proofs are, as far as we can tell, new, and require only elementary results about quasiconformal mappings. 相似文献
15.
胡建勋 《数学物理学报(B辑英文版)》2006,26(4):735-743
In this article, using the WDVV equation,the author first proves that all Gromov-Witten invariants of blowups of surfaces can be computed from the Gromov-Witten invariants of itself by some recursive relations. Furthermore, it may determine the quantum product on blowups. It also proves that there is some degree of functoriality of the big quantum cohomology for a blowup. 相似文献
16.
Xiliang WANG 《Frontiers of Mathematics in China》2021,16(4):1075
Using the degeneration formula, we study the change of Gromov-Witten invariants under blow-up for symplectic 4-manifolds and obtain a genus-decreasing relation of Gromov-Witten invariant of symplectic four manifold under blow-up. 相似文献
17.
Kevin Costello 《Advances in Mathematics》2007,210(1):165-214
This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These Gromov-Witten type invariants depend on a Calabi-Yau A∞ category, which plays the role of the target in ordinary Gromov-Witten theory. When we use an appropriate A∞ version of the derived category of coherent sheaves on a Calabi-Yau variety, this constructs the B model at all genera. When the Fukaya category of a compact symplectic manifold X is used, it is shown, under certain assumptions, that the usual Gromov-Witten invariants are recovered. The assumptions are that open-closed Gromov-Witten theory can be constructed for X, and that the natural map from the Hochschild homology of the Fukaya category of X to the ordinary homology of X is an isomorphism. 相似文献
18.
Guangcun Lu 《Israel Journal of Mathematics》2006,156(1):1-63
We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities.
As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate
it in terms of Gromov-Witten invariants. The (pseudo) symplectic capacities of Grassmannians and some product symplectic manifolds
are computed. As applications we first derive some general nonsqueezing theorems that generalize and unite many previous versions
then prove the Weinstein conjecture for cotangent bundles over a large class of symplectic uniruled manifolds (including the
uniruled manifolds in algebraic geometry) and also show that any closed symplectic submanifold of codimension two in any symplectic
manifold has a small neighborhood whose Hofer-Zehnder capacity is less than a given positive number. Finally, we give two
results on symplectic packings in Grassmannians and on Seshadri constants.
Partially supported by the NNSF 10371007 of China and the Program for New Century Excellent Talents of the Education Ministry
of China. 相似文献
19.
We study relative Gromov-Witten theory via universal relations provided by the degeneration and localization formulas. We find relative Gromov-Witten theory is completely determined by absolute Gromov-Witten theory. The relationship between the relative and absolute theories is guided by a strong analogy to classical topology.As an outcome, we present a mathematical determination of the Gromov-Witten invariants (in all genera) of the Calabi-Yau quintic 3-fold in terms of known theories. 相似文献
20.
Floor diagrams are combinatorial objects which organize the count of tropical plane curves satisfying point conditions. In this paper we introduce Psi-floor diagrams which count tropical curves satisfying not only point conditions but also conditions given by Psi-classes (together with points). We then generalize our definition to relative Psi-floor diagrams and prove a Caporaso-Harris type formula for the corresponding numbers. This formula is shown to coincide with the classical Caporaso-Harris formula for relative plane descendant Gromov-Witten invariants. As a consequence, we can conclude that in our case relative descendant Gromov-Witten invariants equal their tropical counterparts. 相似文献